1 . 如图,正方形
边长为
,以
为圆心,
为半径的圆弧与以
为直径的半圆
交于点
,连结
并延长交
于点
.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/070efbd967784b7bb09a6176db944c29.png)
(1)求证:
为
的中点;
(2)求
的值.
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/57453c6f2806415dab410ba1b4f05cef.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/4455298339f64896b359b953d34294b8.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/6f45f2742cd04744a8e8bb95ad17f554.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/82f15f28b652475c8344ca151698aead.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/066228d43a0840e1a4d89cff04c0be44.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/477875ee3fcf4557b30a82e77722757e.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/4a77b55c5c784fd4aab7506b11c35474.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/7b95841e2cdb41ee80ed7e631a4fa4e9.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/ac61771f1a8b4e66b90926c0dc33c8a3.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/92437732da6c448da5bf61877e777755.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/070efbd967784b7bb09a6176db944c29.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/92437732da6c448da5bf61877e777755.png)
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/ac61771f1a8b4e66b90926c0dc33c8a3.png)
(2)求
![](https://img.xkw.com/dksih/QBM/2016/7/22/1572933430534144/1572933436997632/STEM/9c2381ceba2e4d8fa62a17436d7892d3.png)
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2 . 如图,延长△ABC的角平分线AD交其外接圆于E,若AD =AB= 1,DE =
,则AC=_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2015/6/16/1572126201487360/1572126207524864/STEM/460448641459437db3c1fec97ab5ba10.png?resizew=144)
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3 . (选修4-1:几何证明选讲)如图,已知直线
切圆
于点
,直线
交圆
于点
、
,若
,
,则圆
的半径长为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff8513b61617aa6b19ad2a764ee3aeae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97e22c9dd88a2510de9e5a309191934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e2868b617c871e18c928c9a573bc8c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bec08679eab52e3a0013abecdd1e6cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97e22c9dd88a2510de9e5a309191934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49de2536004d4f0819e781fffca41a2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad4b3ac161685fc1c03f5591b3ccc1d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc17edc472b148dc491f978333d3bdee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97e22c9dd88a2510de9e5a309191934.png)
![](https://img.xkw.com/dksih/QBM/2015/3/30/1572047081906176/1572047087263744/STEM/3226845ff076414f97aabeceed7ba595.png?resizew=160)
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